The mid-point of the line segment joining (4a, 2b - 3) and (-4, 3b) is (2, -2a). Find the values of a and b.

Open in App

Solution

It is given that the mid-point of the line-segment joining (4a, 2b – 3) and (-4, 3b) is (2, -2a).
$left parenthesis 2 comma negative 2 a right parenthesis equals open parentheses fraction numerator 4 a minus 4 over denominator 2 end fraction comma fraction numerator 2 b minus 3 plus 3 b over denominator 2 end fraction close parentheses 2 equals fraction numerator 4 a minus 4 over denominator 2 end fraction 4 a minus 4 equals 4 4 a equals 8 a equals 2 A l s o minus 2 a equals fraction numerator 2 b minus 3 plus 3 b over denominator 2 end fraction minus 2 cross times 2 equals fraction numerator 5 b minus 3 over denominator 2 end fraction 5 b minus 3 equals negative 8 5 b equals negative 5 b equals negative 1$

Suggest Corrections

Similar questions

(2 a, 4)

(- 2, 2 b)

(1, 2 a + 1)

a

b

(a, b)

(a + 2 b, 2 a - b)

If $(a, b)$ is the mid-point of the line segment joining the points $A (10, 6)$ and $B (k, - 4)$ and $a + 2 b = 18,$ find the value of $k .$

(2 a, 4)

(- 2, 2 b)

(1, 2 a + 1)

The mid-point of the line segment joining $(a + b - c, 2 a)$ and $(2 a - b + c, 2 b)$ is $(6, 4)$ . Then the values of $a$ and $b$ respectively are

Join BYJU'S Learning Program